A transversal intersects two lines in such a way that the two interior angles on the same side of the transversal are equal. Will the two lines always be parallel? Give reason for your answer
Solution:
We know that
Two lines will not be parallel as the sum of two equal angles will not be equal to 180°
When each equal angle is equal to 90° the lines will be parallel
Therefore, the two lines will not be parallel.
✦ Try This: Angles of a triangle are in the ratio 8 : 3 : 1. The smallest angle of the triangle is
Given, the angles of a triangle are in the ratio 8: 3: 1
We have to find the smallest angle of the triangle.
We know that the sum of all three interior angles of a triangle is always equal to 180°
Let us consider a triangle ABC
∠A + ∠B + ∠C = 180°
Given, ∠A = 8x
∠B = 3x
∠C = 1x
So,8x + 3x + x = 180°
12x = 180°
x = 180°/12
x = 15°
Now, ∠A = 8(15) = 120°
∠B = 3(15) = 45°
∠C = 15°
Therefore, the smallest angle of the triangle is 15°.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.2 Sample Problem 2
A transversal intersects two lines in such a way that the two interior angles on the same side of the transversal are equal. Will the two lines always be parallel? Give reason for your answer
Summary:
A transversal intersects two lines in such a way that the two interior angles on the same side of the transversal are equal. The two lines will be parallel when each equal angle is equal to 90°
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